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Could it be: https://en.wikipedia.org/wiki/Doraemon_the_Movie:_Nobita%27s_Treasure_Island
Well, maybe not, because this looks recent and the Jim Hawkins-stand-in is the only animal, it seems.
Doraemon has a Treasure Island adaptation now? Must be sure to check it out.
But no, I found it! It turns out it really was The Legends of Treasure Island, but only kind of- in 1997 someone stuck the first three episodes together with the last episode of the first season, for some reason, and released that as a complete movie! It's called, just, Treasure Island, of course, just as I remember it, and... not everything's exactly as I remember it, the dart thing is slightly less ridiculous in context (but still pretty nonsensical and doesn't even matter in the end anyway.)
I’ve got bizarrely specific memories of this- I could have sworn it was named Treasure Island, but it’s not listed among any list of adaptations I can find. I think it was an anime, and an older one (1980s-ish?) An Anthropomorphic Animal Adaptation of Treasure Island, but In Name Only. It’s not The Legends of Treasure Island, but very similar. It’s not Animal Treasure Island either; no human characters at all. Jim Hawkins is a cat in this one, I think. He gets the map, but in this bizarre arbitrary detail it doesn’t show where in the ocean the island even is, so Squire Trelawney says, “then we shall let the gods decide!” and throws a dart at a map of the world and they sail to that place and happen to get it right, the island happens to be right where the dart landed. At one point on the island they’re on a lake or river and there’s an “undertow” (not sure if that’s what they call it in the film or if it’s just my childhood understanding of the events) but it’s a living creature and Jim dives/gets pulled underwater by it, and gets to see the entire thing, which turns out to be some nightmarish anemone-like tentacle monster on the bottom of the lakebed. At the end of the movie, they never find the treasure and the island sinks into the sea and it’s incredibly depressing.
Edited by Pretzels